Problem: Rewrite as a simplified fraction. ${1.\overline{93} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 193.9393...\\ 1x &= 1.9393...\end{align*}}$ Subtracting the two equations, we have: ${99x = 192}$ ${x = \dfrac{192}{99}} $ ${x = \dfrac{64}{33}} \text{or} {1 \dfrac{31}{33}}$